‎Mathématiques‎

‎"CAUCHY, AUGUSTIN. - CAUCHY'S THORY OF EQUIVALENCES.‎

‎Mémoire sur une nouvelle théorie des imaginaires, et sur les racines symboliques des équations et des équivalences.‎

‎(Paris, Bachelier), 1847. 4to. Without wrappers. In ""Comptes rendus hebdomadaires des séances de l’Académie des sciences"", Vol. 24, No 26. Pp. (1117-) 1160. (Entire issue offered). Cauchy's paper: pp. 1120-1130.‎

‎First apperance of this impiortent paper in which Cauchy presents his theory of algebraic equivalences where imaginary numbers were regarded as equivalent classes of polynominals with real coefficients modulo (X2 + 1).The paper gave rise to a heated debate in the Academy (see Bruno Belhoste ""Augustin-Louis Cauchy. A Biography."" pp. 210 ff.).""Augustin Louis Cauchy... objects to the use of complex or imaginary numbers and finds a method of eliminating i (the square root of negative 1) by constructing residues to the modulus X2 + 1. These residues have the formal properties of the complex number system, with x replacing i."" (Parkinson ""Breakthroughs, 1847 M).‎

书商的参考编号 : 47261

‎"GUDERMANN, CHRISTOPH.‎

‎Theorie der Potenzial- oder der cyklisch- hyperbolischen Functionen. (Fortsetzung der Abhandlung No. 1. im vorigen Hefte). - [GUDERMANNIAN FUNCTION]‎

‎Berlin, G. Reimer, 1830. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 6. Band, 1830""., without backstrip. Fine and clean. [Gudermann:] Pp. 162-194. [Entire volue: Pp. 147-214].‎

‎First printing of Gudermann extensive and important second paper on hyperbolic functions. During 1830ies Gudermann focused his work on these functions and published extensive on the subject, the present paper being the first. It was later coined the Gudermannian function.The function was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions. He called it the ""transcendent angle,"" and it went by various names until 1862 when Cayley suggested it be given its current name as a tribute to Gudermann's work in the 1830ies on the theory of special functions. The present paper together with two later published papers were collected in Theorie der potenzial- oder cyklisch-hyperbolischen functionen (1833), a book which expounded sinh and cosh to a wide audience.The issue also contain a paper by the famous Norwegian mathematician Niels Henrik Abel.""Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written."" (DSB).Gudermann is known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions in 1839, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.‎

书商的参考编号 : 47281

‎"KUMMER, E. E.‎

‎Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen.‎

‎Berlin, G. Reimer, 1827. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 2. Band, 1827""., without backstrip. Fine and clean. [Gudermann:] Pp. 223-226. [Entire volue: Pp. 198-292 + two folded plates].‎

‎First printing of Kummer's paper on Transcendental Numbers.‎

书商的参考编号 : 47283

‎"HERMITE, CHARLES (+) JACOBI.‎

‎Extraits de deux lettres de M. Charles Hermite a M. Jacobi. - [THE VERY FIRST RESEARCH BY HERMITE]‎

‎Berlin, G. Reimer, 1846. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 32. Band, 1846"". Entire issue offered.‎

‎First appearance of these two fundamental letters, representing the very first research by Hermite, sent from Charles Hermite to Jacobi"" the letter first in January 1843, the second in august 1944. Hermite's first letter is on the extension of Abelian functions of the theorem given by Abel on the division of the argument of elliptic functions and begins as follows: ""The study of your memoir published in Crelle's journal under the title 'De functionibus quadruliciter periodicis quibus theoria transcendentium Abelianarum innititur' has led me, for the division of the argument in these functions to a theorem analogous to that which you have given in the third volume of that journal for obtaining the simplest expression of the roots of the equation treated by Abel"". Hermite shows that the corresponding equations are soluble by radicals and he treats of the reduction of the equation in the case of the division of complete functions. Hermite's second letter gives the proof of the formula for the transformation of elliptic functions which Jacobi had given without proof six years before. ""These two letters, embodying as they do the first original researches of Hermite, were given by Jacobi the same cordial reception as had been accorded to his first letter of 1827 by Legendre. Writing on the 24th June, 1843, in reply to Hermite's first letter, Jacobi says ""I thank you very sincerely for the beautiful and important communication which you have made to me about the division of Abelian functions. You have opened, by the discovery of this division, a vast field of researches and new discoveries which will give a great impetus to the analytical art."" (Prasad, Some Great Mathematicians of the Nineteenth Century).‎

书商的参考编号 : 47328

‎"JACOBI, C. G. J.‎

‎De tranformatione integralis duplicis indefiniti in formam simpliciorem (I + II).‎

‎[Berling, G. Reimer, 1831]. 4to. As extracted, without backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 1831. Fine and clean. Pp. 253-279" Pp. 321-357.‎

‎First printing.‎

书商的参考编号 : 47331

‎"LIOUVILLE, JOSEPH.‎

‎Mémoire sur une formule d'analyse.‎

‎[Berlin, G. Reimer, 1834.] 4to. As extracted, without backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 12. Band, 1834"". Fine and clean. Pp. 273-87. [Entire offering: Pp. 273-364].‎

‎First printing of Liouville's important comment to his earlier memiore ""Sur quelques questions de Géometrie et de Mécanique"". ""Liouville is most famous for having founded and directed for almost forty years one of the major mathematical journals of the nineteenth century, the Journal de Liouville. He also made important contributions in pure and applied mathematics and exerted a fruitful influence on French mathematics through his teaching."" (DSB).‎

书商的参考编号 : 47374

‎"CAYLEY, ARTHUR.‎

‎Note on a Family of Curves of the Fourth Order.‎

‎Cambridge, Macmillan and Co., 1850. 8vo. Bound in contemporary half calf with black and red title labels to spine with gilt lettering. In ""The Cambridge and Dublin Mathematical Journal"", Vol. V [5], (Being Vol. IX [9], of the Cambridge Mathematical Jorunal), 1850. Bookplate pasted on to pasted down front free end-paper and library code written in hand to lower part of spine. Library cards in the back. A fine and clean copy. Pp. 148-59. [Entire volume: IV, 288 pp.].‎

‎First printing of Cayley's important paper on curves of the fourth order. ""As an example of a remarkable property of cubic surfaces there was Cayley's discovery in 1849 [the present paper], of the existence of exactly 27 lines on every surface of the third degree. Not all need be real but there are surfaces for which they are all real."" (Kleine, P. 859).The volume contains many other important contributions by contemporary mathematicians.‎

书商的参考编号 : 47401

‎"STEICHEN, E.‎

‎Exposé de diverses remarques et reflexions sur les moments et d'autres sujets de statique.‎

‎Berlin, Georg Reimer, 1852. 4to. In the original wrappers, without backstrip. In ""Journal für die reine und angewandte Mathematik"", 44 band, 3. heft. Entire issue offered. Fine and clean. Pp. 181-219. [Entire issue: Pp. 181-276 + 2 folded plates].‎

‎First printing.‎

书商的参考编号 : 47447

‎"PERRON, OSKAR.‎

‎Zur Theorie der Matrices. - [Perron-Frobenius theorem]‎

‎Leipzig, B. G. Teubner, 1907. 8vo. Bound in contemporary half calf with gilt lettering to spine. In ""Mathematische Annalen"", 64. Band, 1907. Hinges and extremities with wear. Bookplates to pasted down front free end-paper. Internally fine and clean. Pp. 248-263. [Entire volume: IV, 576 pp].‎

‎First printing of Perron's important paper on positive matrices which profoundly influenced several fields of science. ""Today the Perron-Frobenius mathematics of nonnegative matrices enjoys wide applications, the most sensational perhaps being its implicit use by millions of internet surfers, who routinely activate Google's PageRank algorithm every day. Such a remarkable worldwide application in an electronic search engine is a far cry from the original theoretical articles, written more than a century ago, by Perron and Frobenius. These two German scholars preferred to concentrate on pure mathematics. Especially Frobenius in Berlin considered applications as inferior subjects that should be relegated to technical schools"" (PARYS, How pioneers of linear economics overlooked Perron-Frobenius mathematics).The volume also contain Hjelmslev's important paper: ""Neue Begründung der ebenen Geometrie"" and Brill's paper on three-dimensional algebraic curves: ""Ueber algebraische Raumkurven"".‎

书商的参考编号 : 47453

‎"OLMSTED, P. S. (+) J. W. TURKEY.‎

‎Testing Peripheral Association. A Corner Test for Association.‎

‎(Atlantic City, N. J., 1947). Large 4to. (278x214 mm / 10.94x8.43 inches). Offprint from Bell System Technical Journal, Vol. 18, pp.495-513, December, 1947. Original printed wrappers with holes punched in the back (as issued). Lower left corner with traces after having been bended. Lower 2 cm of spine loosened, otherwise fine and clean throughout. Pp. 19.‎

‎Scarce offprint issue of Olmstead and Tukey's important paper in which a new method for the association of two continuous variables are proposed. ""Its notable properties are: (1) Special weight is given to extreme values of the variables. (2) Computation is very easy. (3) The test is non-parametric."" (From the present paper). ""One of the most influential statisticians of the twentieth century, John Wilder Tukey (1915-2000) played a key role in both the development and study of statistics. Upon receiving his Ph.D. in mathematics in 1939 from Brown University, he joined the faculty at Princeton"" in 1945, he also began work at Bell Laboratories. Equally committed to both Princeton and Bell Labs, Tukey chose to work concurrently at both institutions. He was also a consultant for many companies, such as Merck and Company, Xerox Corporation, and the Educational Testing Service, and was a frequent advisor to the government for such programs as the US Census. From 1960 to 1980 he led the statistical component of NBC's election night projections. Among other projects Tukey analyzed Alfred Kinsey's research and examined data on ozone depletion. Tukey made many important contributions to the field of statistics, such as work in time series analysis, exploratory data analysis, and multiple comparisons. In early 1945, Tukey began working for Bell Labs, a lifelong association, as it would turn out. While at Bell Labs, Tukey worked with B. D. Holdbrook to develop the Nike missile system although the scant correspondence within this collection is rather routine and doesn't reflect their extensive contribution. Tukey also had a reputation for being discreet regarding his more sensitive projects."" (American Philosophical Society).‎

书商的参考编号 : 47529

‎"JACOBI, C. G. J.‎

‎Nota de erroribus quibusdam geometricis, qui in theoria fonctionum leguntur.‎

‎Berlin, G. Reimer, 1837. 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 16. band, Heft 4, 1837. Entire fourth heft offered. Fine and clean. Pp. 342-3. [Entire volume: Pp. 285-376 + 1 folded plate].‎

‎First printing. ""Most of Jacobi’s fundamental research articles in the theory of elliptic functions, mathematical analysis, number theory, geometry, and me-chanics were published in Crelle’s Journal fue die reine and angewandte Mathematik. With an average of three articles per volume, Jacobi was one of its most active contributors and quickly helped to establish its international fame."" (DSB).‎

书商的参考编号 : 47531

‎"RICHELOT, FRIEDRICH JULIUS.‎

‎De transformatione integralium Abelianorum primi ordinis commentatio.‎

‎Berlin, G. Reimer, 1836 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 16. band, Heft 3, 1836. Entire first heft offered. Fine and clean. Pp. 221-84. [Entire volume: Pp. 197-84].‎

‎First printing of Richelot's important contribution to the theory of abelian varieties in algebraic geometry.‎

书商的参考编号 : 47533

‎GUDERMANN, CHR.‎

‎Fundamenta Trigonometriae sphaeroidicae exacta" imprimis de lineis brevissimis, vulgo dictis geodaeticis, in superficie sphaeroidica.‎

‎Berlin, G. Reimer, 1852. 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 43. band, Heft 4, 1852. Entire fourth heft offered. Fine and clean. Pp. 294-339. [Entire volume: Pp. 283-374 + 3 plates.].‎

‎First printing.‎

书商的参考编号 : 47535

‎"CLAUSIUS, R. (RUDOLF)‎

‎Über die Intensität des durch die Atmosphäre reflectirten Sonnenlichts.‎

‎Berlin, G. Reimer, 1848. 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 36. band, Heft 3, 1848. Entire third heft offered. Fine and clean. Pp. 185-244. [Entire volume: Pp. 185-282 + 3 plates.].‎

‎First printing of Clausius early and important paper on the influence of the atmosphere on sunlights.""In one paper, dealing mainly with the problem of reflected light in the sky, Clausius’ distinctive approach to many physical questions was already apparent: an excellent grasp of the fundamental facts and equations relevant to the phenomena, a microscopic model to account for them, and an attempt to correlate the two with mathematics. For example, Clausius imagined that the blue color of the sky arose from the preferential reflection of blue light from thin films of water. He postulated, therefore, the existence of water bubbles in the earth’s atmosphere and investigated mathematically the requisite conditions of number, size, and thickness."" (DSB).‎

书商的参考编号 : 47537

‎"JACOBI, C. G. J.‎

‎Note sur une nouvelle application de l'analyse des fonctions elliptiques à l'algèbre.‎

‎Berlin, G. Reimer, 1831. 4to. Contemporary binding with marbled paper over boards. In ""Journal für die reine und angewandte Mathematik"", 7. band, Heft 1, 1831. Entire heft 1. offered. Fine and clean. Pp. 41-43. [Entire offered volume: IV, 104 pp.].‎

‎First printing of Jacobi's paper on elliptic function theory.‎

书商的参考编号 : 47539

‎"OETTINGER, L.‎

‎Summenrechnung für einfache und zusammengesetzte Reihen, gegründet auf die Differenziale und Integrale der Functionen, wodurch die Reihen erzeugt werden.‎

‎Berlin, G. Reimer, 1836. 4to. In the original printed wrappers, without back strip. In ""Journal für die reine und angewandte Mathematik"", 16. band, Heft 2, 1836. Entire second heft offered. Fine and clean. Pp. 131-191. [Entire volume: Pp. 97-196 plates.].‎

‎First printing.‎

书商的参考编号 : 47657

‎"PAINLEVÉ, PAUL. - INTRODUCING THE PAINLEVÉ TRANSCENDENTS.‎

‎Sur les équations differentielles du second ordre à points critiques fixes.‎

‎(Paris, Gauthier-Villars), 1906. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 143, No 26.. Pp. (1110-) 1208. (Entire issue offered). Painlevé's paper: pp. 1111-1117. Frayed in inner margins, poor paperquality.‎

‎First apperance of the paper in which Pailevé introduced the transcendents which bears his name.""The phenomenon of movable singular points was discovered by Fuchs. The study of movable singular points and of nonlinear second orderr equations with and without such singular points was taken up by many men, notably by Paul Painlevé."" (Morris Kline ""Mathematical Thought from Ancient to Modern Times"", p. 737).‎

书商的参考编号 : 47894

‎"PASCH, MORITZ.‎

‎Mathematik am Ursprung. Gesammelte Abhandlungen über Grundfragen der Mathematik.‎

‎Leipzig, Felix Meiner, 1927. Orig. printed wrappers. Frontwrapper loose. Small loss to top of backstrip. (4),149 pp. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper.‎

‎First edition of this collection of 7 of Pasch's most importent work on axiomatics and geometry.""Pasch initiated the axiomatic method, although the foundational developments of his time were against this point of view. Thus Cantor's striking discoveries were based, from an axiomatic point of view, on nothing... As late as 1903 Frege poked fun of at the axiomatic method as presented in Hilbert's ""Grundlagen der Geometrie....particularly Peano continued Pasch's work. In 1889 Peano published both his exposition of geometry, following Pasch, and his treatment of number...Pasch played a crucial role in the innovation of the axiomatic methode. This method, with contributions from logic and algebra, is a central feature of twentieth-century mathematics."" (DSB).‎

书商的参考编号 : 47944

‎KLEIN, FELIX.‎

‎Lectures on Mathematics delivered from Aug. 28 to Sept. 9, 1893 before members of the Congress of Mathematics held in Connection with the World's Fair in Chicago at Northwestern University. Reported by Alexander Ziwet.‎

‎New York, American Mathematical Society, 1911. Orig. full cloth. Stamps on foot of titlepage. IX,(2),109 pp. Clean and fine. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on front free endpaper.‎

书商的参考编号 : 47947

‎PASCH, MORITZ. - MAX DEHN.‎

‎Vorlesungen über Neuere Geometrie. Zweite Auflage. Mit einem Anhang: Die Grundlegung der Geometrie in historischer Entwicklung. Mit ingesamt 115 Abbildungen.‎

‎Berlin, Julius Springer, 1926. Orig. full cloth. Stamps on titlepage. X,275 pp. Internally clean and fine. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on front free endpaper.‎

‎Pasch's classic work from 1882 is here published together with Dehn's historical paper.‎

书商的参考编号 : 47950

‎LAMOUCHE, ANDRÉ.‎

‎La Théorie Harmonique. Le Principe de Simplicité dans la Mathématiques et dans les Sciences Physiques.‎

‎Paris, Gauthier-Villars, 1955. Orig. printed wrappers. Small nick to frontwr. Stamps on foot of titlepage. 481 pp. Internally clean and fine. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper.‎

书商的参考编号 : 47982

‎HÖLDER, OTTO.‎

‎Anschauung und Denken in der Geometrie. Akademische Antrittsvorlesung gehalten am 22. Juli 1899. Mit Zusätzen, Anmerkungen und einem Register.‎

‎Leipzig, B.G. Teubner, 1900. Hcloth with gilt lettering to spine. Stamps to foot of titlepage and on last page. 6 margins with contemp. annotations, otherwise clean. (2),75 pp.‎

‎First edition of Hölder's inaugural lecture when he succeeded Sophus Lie in Leipzig.‎

书商的参考编号 : 47986

‎"JACOBI, C. G. J.‎

‎Auszug aus einem Schreiben des Herrn Prof. Dr. C. G. J. Jacobi zu Königsberg i. Pr., an den Herrn Prof. Dr. J. Steiner zu Berlin.‎

‎[Berlin, G. Reimer, 1834]. 4to. Without wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 1834, Pp. 137-140. [Entire offering: Pp. 137-180].‎

‎First printing.‎

书商的参考编号 : 48005

‎PETERSEN, JULIUS.‎

‎Lehrbuch der Stereometrie. In deutsche übersetzt unter Mitwirkung von R.von Fischer-Benzon.‎

‎Kopenhagen, Höst & Sohn, 1885. Uncut in orig. printed wrappers. Stamps on titlepage. 94 pp., textillustr. From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper.‎

书商的参考编号 : 48030

‎"MINDING. [ERNST FERDINAND ADOLF].‎

‎Ueber die Bestimmung des Grades einer durch Elimination hervorgehen den Gleichung.‎

‎Berlin, G. Reimer, 1841. 4to. In ""Journal für die reine und angewandte Mathematik, 22. Band, 2 Heft, 1841"". In the original printed wrappers, without backstrip. Fine and clean. [Minding:] Pp. 178-83. [Entire volume: Pp. 97-192, (2)].‎

‎First printing of Minding's important paper in which he presents his theorem representing the first (implicit) appearance of the BKK bound and some of its extensions in the amthematical literature. ""Minding's most important discoveries were in the dilierential geometry of surfaces"" in these works he brilliantly continued the researches of Gauss, which had been published in 1828. In his first paper (1830), which dealt with the isoperimetric problem of determining on a given surface the shortest closed curve surrounding a given area (on the plane it is the circumference of a circle), he introduced the concept of geodesic curvature. It was independently discovered in 1848 by O. Bonnet, and it was he who named it geodesic curvature. Minding soon proved, as did Bonnet after him, the invariance of the geodesic curvature under bending of the surface. Neither of them knew that the same results had been presented in an earlier, unpublished paper of Gauss's (1825)."" (DSB).‎

书商的参考编号 : 48042